Ahsan A. (ed.) Evaporation, Condensation and Heat transfer

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Modelling the Thermo-Hydraulic Performance of

Cooling Networks and Its Implications on Design, Operation and Retrofit

199

For every exchanger specify: t’s, T’s,

V’s, ΔP

allowable

, Q, F

For the network specify: valve’s, d

pipe’s

, pump

capacity, N

, L

, d

Calculate K for valves and pipes

Assume number of tubes (Nta) and

calculate K for heat exchangers

Calculate ΣK

pipe, valve, Cx

for each single branch

Calculate K for network

arrangement and K

overall-system

Calculate ΔP

system

Calculate flow distribution

Specify K

Cx’s-req

= f(ΔP

allow

, F

) and compare with K

Calculate t

out’s

= f(Q

Cx-req

, t

, V

)

Calculate temperature correction

factor

Calculate h

, h

and U

overall

Calculate LMTD’s

Calculate heat transfer

area, A

Cx’s

Calculate number of tubes, Nt

End

Modify

number of

tubes

Nt = Nta

For every exchanger specify: t’s, T’s,

V’s, ΔP

allowable

, Q, F

For the network specify: valve’s, d

pipe’s

, pump

capacity, N

, L

, d

Calculate K for valves and pipes

Assume number of tubes (Nta) and

calculate K for heat exchangers

Calculate ΣK

pipe, valve, Cx

for each single branch

Calculate K for network

arrangement and K

overall-system

Calculate ΔP

system

Calculate flow distribution

Specify K

Cx’s-req

= f(ΔP

allow

, F

) and compare with K

Calculate t

out’s

= f(Q

Cx-req

, t

, V

)

Calculate temperature correction

factor

Calculate h

, h

and U

overall

Calculate LMTD’s

Calculate heat transfer

area, A

Cx’s

Calculate number of tubes, Nt

End

Modify

number of

tubes

Nt = Nta

Fig. 6. Algorithm for the thermo-hydraulic design of a cooling network.

6. Case study

Using the principles introduced in the sections above, the design of a flexible cooling system

will be looked at in more detail. A cooling system is designed to operate for a range of plant

throughputs, namely: 120%, 100% and 80%. Heat exchangers are initially designed for the

maximum production rate where the cooling demand is 3.65 MW; cooling water is available

at 20°C and the maximum return temperature is 40°C with a water flow rate of: 0.0438

m3/s. The process information for the streams is given in Table 2. The allowable pressure

drops, water flow rates and the corresponding K values are presented in Table 3. In Table 4

the geometry of the exchangers such as the tube passes, tube length and tube inner and

outer diameter and the K values for the case of water control valves are also given. The

Evaporation, Condensation and Heat Transfer

200

information related to the pipe lengths, diameters, heights and control valves is provided in

Table 5. When the various components of the system are brought together, the cooling water

is redistributed which in turn affects the thermal performance of the exchangers. So, the new

water distribution is determined and the results are given in Table 6. The calculated

pressure drops through branches are shown in Table 6.

Stream

Inlet

temperature (°C)

Outlet

temperature (°C)

(W/°C)

Heat duty

(kW)

H1 50 30 8 400

H2 50 40 42.53 1,014

H3 85 40 16.8 1,906

H4 85 65 4.24 205

C1 20 40 5.14 400

C2 20 40 12.85 1,014

C3 20 40 23.13 1,906

C4 20 40 2.57 205

Table 2. Stream process data.

Exchanger

ΔPallowable

(kPa)

Water flow rate

(m3/s)

Cx1 40 0.0052 285,239

Cx2 40 0.0129 330,432

Cx3 40 0.0232 117,771

Cx4 40 0.0026 6,162,219

Table 3. Pressure drop, water flow rate and K values for heat exchangers.

Exchanger Cx1 Cx2 Cx3 Cx4

K valve 9 9 9 9

No. Passes 2 2 2 2

length, m 6.1 6.1 6.1 6.1

tube i.d., m 0.0148 0.0148 0.0148 0.0148

tube o.d., m 0.01905 0.01905 0.01905 0.01905

Table 4. Geometrical parameters of heat exchangers.

Branch

Diameter

(m)

Length

(m)

Heigh

(m)

Kvalve

Feed 0.35 220 0 9

A 0.25 120 5 9

B 0.25 170 7 9

C 0.2 180 10 9

D 0.2 190 10 9

Return 0.35 220 0 55

Table 5. Geometry and dimensions of the various components of the piping system.

Modelling the Thermo-Hydraulic Performance of

Cooling Networks and Its Implications on Design, Operation and Retrofit

201

Branch

Water flow rate

(m3/s)

Pressure drop

(kPa)

A 0.0020 40.03

B 0.0186 42.19

C 0.0112 41.95

D 0.0121 42.30

Total flow rate 0.0438

Table 6. Water flow rate re-distribution through branches.

Under these conditions, the design of the heat exchangers has to be revisited and new

dimensions determined for each exchanger. What is sought is that each exchanger removes

the required heat load; on achieving this target, the water outlet temperature in some cases

goes above the established limit of 40°C. The relation between surface area and K values can

be seen in Tables 3 and 7; exchanger Cx3 has the largest surface area and the lowest K value,

the opposite applies to exchanger Cx4 that exhibits the smallest surface area and largest K

value.

Cx1 Cx2 Cx3 Cx4

out

(°C) 27.92 41.70 44.43 44.91

ΔP (kPa)

40.00 40.00 40.00 40.00

Surface Area (m2) 130 110 196 14

No. of tubes 356 301 537 37

Table 7. Revisited geometry of heat exchanger for the final water flow rate distribution.

The thermo-hydraulic model described in this work is used to demonstrate the flexible

operation of the cooling system; for the various scenarios the process stream flow rates are

multiplied by the required factors to simulate the increase or reduction in production rate.

The network presented in Figure 1 is used as case study. Tables 8, 9 and 10 show the

network water flow rates and temperatures for 120%, 100% and 80% throughput

respectively.

Water

temperatures (°C)

Process

temperatures (°C)

Branch

Inlet Outlet Inlet Outlet

Total tower

cooling load

(MW)

Cooling

water

/s)

System

bypass

/s)

A 20 28.29 50 29.05 0.0121

B 20 41.72 50 39.9 0.0111

C 20 45.6 85 37.7 0.0186

D 20 45.6 85 64.5

3.65

0.0020

0.0

Water return

temperature

39.8

Water

flow

rate (m

/s)

0.0438

Table 8. Water flow rate distribution and stream temperatures for a 120% plant throughput.

Evaporation, Condensation and Heat Transfer

202

Water

temperatures (°C)

Process

temperatures (°C)

Branch

Inlet Outlet Inlet Outlet

Total tower

cooling load

(MW)

Cooling

water

/s)

System

bypass

/s)

A 20 30.4 50 28.9 0.0081

B 20 43.9 50 41.17 0.0074

C 20 50.15 85 40.6 0.0124

D 20 52.7 85 64.06

2.85

0.0013

0.0146

Water return

temperature

43.2

Water

flow rate

/s)

0.0292

Table 9. Water flow rate distribution and stream temperatures for a 100% plant throughput.

Since the scenarios that are analyzed consider seasonal variations in plant production, it is

acceptable to consider that instead of just recycling water back to the cold pond, pumps can

be taken out of operation for 100% and 80% plant throughput. For instance, six pumps can

be selected for the condition of 120%. When production returns to 100%, one pump is taken

out of operation. Further decrease in throughput to 80% is accompanied by the shutting

down of a second pump.

Water

temperatures (°C)

Process

temperatures (°C)

Branch

Inlet Outlet Inlet Outlet

Total tower

cooling load

(MW)

Cooling

water

/s)

System

bypass

/s)

A 20 32.9 50 29.51 0.005

B 20 45.6 50 42.59 0.0046

C 20 55.07 85 44.39 0.0078

D 20 61.16 85 64.34

2.05

0.0008

0.0256

Water return

temperature

46.82

Water

flow rate

/s)

0.0182

Table 10. Water flow rate distribution and stream temperatures for a 80% plant throughput.

7. Determining the performance under changed cooling water temperature

Flexible operation can be extended to situations where the ambient conditions affect the

performance of a cooling tower; for instance: variation in the wet bulb temperature. The

model is used to simulate the case study given in Table 2. The simulation proceeds by

assuming a change in the inlet temperature of the cooling water; the effect upon the outlet

temperatures is determined and then the water flow rate is changed in order to restore the

process stream target temperatures.

Table 11 shows the case where the inlet temperature is 24°C and 18°C respectively. When

the temperature of the cooling water increases to 24°C, the simulation shows that increasing

the water flow rate by 8%, the process outlet temperatures can be restored to acceptable

values as shown in Table 12.

Modelling the Thermo-Hydraulic Performance of

Cooling Networks and Its Implications on Design, Operation and Retrofit

203

The water return temperature for this case is 35.49°C and the cooling load 3.47 MW. Now,

for the case where the cooling water enters at 18°C to the system, the heat removal rate will

be higher than required. Therefore, the solution consists in reducing the flow rate. Table 13

shows the thermal performance of the exchangers; the cooling duty for this case is 3.53 MW

and the water return temperature is 41.4°C. Since the performance is within acceptable

values, the system needs not to adjust its water flow rate.

Cooling water: 24°C Cooling water : 18°C

Unit Tout (°C) tout (°C) Unit Tout (°C) tout (°C)

Cx1 31.85 31.18 Cx1 27.66 26.84

Cx2 41.32 42.82 Cx2 39.32 41.16

Cx3 41 48.06 Cx3 36.32 44.42

Cx4 65.65 48.22 Cx4 63.75 44.6

Table 11. Temperature response at different cooling water inlet temperatures.

Cooling water: 24°C

Unit

Process stream

Tout (°C)

Process stream

Target (°C)

Cooling water

tout (°C)

Cx1 31.4 30 30.4

Cx2 40.6 40 41.87

Cx3 39.1 40 46

Cx4 65 65 46

Table 12. Process outlet temperatures after increasing water flow rate by 8%.

Cooling water: 18°C

Unit

Process stream

Tout (°C)

Process stream

Target (°C)

Cooling water

tout (°C)

Cx1 28.48 30 28.4

Cx2 40.6 40 42.85

Cx3 39.33 40 48

Cx4 64.93 65 48.6

Table 13. Thermal performance after reduction of cooling water temperature.

8. Conclusions

Cooling systems are, in most applications, designed for a maximum fixed heat duty and

its operation remains unchanged despite the variations in plant throughput. A

disadvantage of this practice is that operating costs tend to be higher than they should be.

Flexible operation is the capacity of the system to deliver the required heat load within

some specific bounds. For instance, specific bounds may be the following: plant

throughput may vary between a minimum and a maximum from normal production rate

and the wet bulb temperature, which significantly affects the performance of a cooling

tower, experiences changes between seasons. When a temperature or flow rate

Evaporation, Condensation and Heat Transfer

204

disturbance enters a cooling system, it propagates around until the steady state is reached.

Since the steady state response of a cooling system is independent of the actual

arrangement of the coolers then the heat load removal can be controlled through the use

of a bypass scheme. With the operation of a flexible cooling system, the pumping power

consumption is a variable that can also be controlled. Typically, the design of a cooling

system is carried out by considering individual components at a time for a given set of

operating conditions; when these components are placed together into a system, the water

flow rate is no longer the same since it tends to re-distribute through the network

depending on the resistance it encounters. The result of this phenomenon is that water

flow rate distributes through the network so that the pressure drop in all branches of the

system equates. So, a thermo-hydraulic model has to be implemented for the

determination of the performance of a cooling system and it can be used to produce a

design that meets the required flexibility. Such a model has been introduced in this work.

9. Nomenclature

A heat exchanger surface area [m

]

Cr heat capacity mass flow rate ratio

C number of coolers in cooling network

min

minimum heat capacity mass flow rate

max

maximum heat capacity mass flow rate

d diameter [m]

h heat transfer coefficient [kJ/m

°C]

logarithmic temperature correction factor

K loss coefficient

Lt tube lengths [m]

M number of mixing point in a cooling network

Nt number of tubes in heat exchanger

Nta number of tubes assumed

NP number passes

NTU number of heat transfer units

NV number of temperature variables in a cooling network

Q heat load [kW]

S number of streams

T hot stream temperature [°C].

t cold stream temperature [°C]

U overall heat transfer coefficient [W/m

°C]

u fluid velocity [m/s]

V volumetric flow rate [m

/s]

Subscripts

s shell side

t tube side

i inner condition

o outer condition

Superscripts

new condition

Modelling the Thermo-Hydraulic Performance of

Cooling Networks and Its Implications on Design, Operation and Retrofit

205

o original condition

m mixing point

Greek letters

ε thermal effectiveness

ΔP pressure drop (kPa)

ρ density [kg/m3]

10. References

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Castro M M, Song T W, Pinto J M (2000). Minimization of operational costs in cooling water

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Chengqin R (2006). An analytical approach to the heat and mass transfer processes in

counterflow cooling towers. Journal of Heat Transfer Transactions of the ASME

128: 1142 – 1148.

EI – Dessouky H T A, AI – Haddad A A, I–Juwayhel F A (1997). Modified analysis of

counter flow wet cooling towers. Journal of Heat Transfer Trans of ASME 119: 617 –

626.

Gharagheizi F, Reza H and Shohreh F (2007). Experimental study on the performance of

mechanical cooling tower with two types of film packing. Energy Conversion and

Management 48: 277 – 280.

Giorgia F, Cortinovis M, Ribeiro T, Paiva J L, Tah S W, Pinto J M (2009). Integrated analysis

of cooling water systems: modeling and experimental validation. Applied Thermal

Engineering 29: 3124–3131.

Jaber H T, Webb R T (1989). Design of cooling towers by the effectiveness – NTU method.

ASME Journal of Heat Transfer 11: 873–843.

Jameel–Ur– Rehman K, Bilal A Q and Syed M Z A (2004). Comprehensive design and

performance evaluation study of counter flow wet cooling towers. International

Journal of Refrigeration 27 : 914–923.

M. Picón Núñez, J. Castro Páez and F. Vizcaíno García (2002). Steady state simulation for the

de-bottlenecking of heat recovery networks. Applied Thermal Engineering 22 :

1673-1687.

Majozi T, Moodley A (2008). Simultaneous targeting and design for cooling water systems

with multiple cooling water supplies. Computers and Chemical Engineering 32:

540–551.

Nenad M, Pertti H (2001). A comprehensive approach to cooling tower design. Applied

Thermal Engineering 21: 899 – 915.

Panjeshahi M H, Ataeib A, Gharaiec M, Parandc R (2009). Optimum design of cooling water

systems for energy and water conservation. Chem Eng Res Des 8: 7 , 200–209.

Perry and Cecil H. Chilton (1999). Fluid particle dynamics. Chemical Engineer’s Handbook,

McGraw Hill.

Picón-Núñez M, Nila-Gasca C, Morales-Fuentes A (2007). Simplified model for the

determination of the steady state response of cooling systems. Applied Thermal

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Evaporation, Condensation and Heat Transfer

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W.M. Kays and A.L. London (1984). Compact heat exchangers, Third edition, McGraw

Hill.

Heat Exchange in Furnace Side Walls with

Embedded Water Cooled Cooling Devices

Gabriel Plascencia

CIITEC –IPN México, D.F.,

México

1. Introduction

Current copper (as well as nickel and lead) smelting and converting are characterized by

high intensity and productivity. However, this has lead to increasing demands on

refractories resulting in possible shortening of the service life of furnace linings. To

counteract this, several cooling systems have been designed and implemented in many

copper and / or nickel making facilities (Hatch & Wasmund, 1974; Legget & Gray, 1996).

The different cooling systems can be grouped according to their ability to remove heat from

the hearth of the furnace as shown in Table 1. Cooling systems that are embedded into the

furnace refractory lining are able to extract more energy (10 ~ 100 kW/m

) than those acting

on the furnace outer shell (~ 1 kW/m

); this main difference is due to the thermal resistance

that the insulating refractory lining offers (Legget & Gray, 1996).

System Location

Heat Flux

(kW/m

)

Applications Pros Cons

Plate

coolers

Internal 10 – 30

Stack region of iron

blast furnaces /

flash smelters

High intensity

cooling,

supports lining

Water leaks,

limited by

structural

considerations

Staves Internal 20 – 30

Stack region of iron

blast furnaces

Applicable in

thin wall

sections

Limited control,

expensive

Internal

jackets

Internal 10 – 30

Flash and electric

furnaces

Cheaper than

plates

Water leaks,

uneven cooling

Panels Internal > 30

Electric furnaces,

Vanyukov bath

smelting, Zn

fuming

No refractory

needed, high heat

fluxes

Water leaks,

develop

mechanical stresses

External

jackets

External 5 – 15

Temporary cooling

for overheated

walls

No need to shut

down

Limited heat flux

in thick sections

Spray

cooling

External 5 – 15

Electric and flash

furnace reaction

shaft

Cheap, no need to

shut down

Corrosion in the

outer shell, limited

heat flux

Air

cooling

External < 10

Underneath of

many furnaces

Cheap,

water free

Very low heat

fluxes

Table 1. Cooling systems industrially available, after Legget and Gray (Legget & Gray, 1996)

Evaporation, Condensation and Heat Transfer

208

Another factor that affects the difference in the heat flux removal is that the systems that are

embedded in the refractory are closer to the furnace’s hot face, reducing the effective heat

transfer distance, thus increasing the ability to remove heat.

Proper cooling system design is necessary since not every smelter runs in the exactly same

manner, as an example, if the side wall heat flux is too low, the refractory may wear back, or

if the cooling is highly intense, the excessive cooling may lead to higher heat losses.

Modern smelting processes such as flash, bath or electric furnace, make external cooling

unsuitable for their implementation, instead embedded systems are required due to their

capacity to extract more heat and thus protect the refractory walls.

Hatch and Wasmund (Hatch & Wasmund, 1974) recognized that refractories are attacked by

several mechanisms, such as melting, dissolution by molten metal/slag, chemical reactions

between the refractory and the slag. They also acknowledged that refractory spalling may

happen as a result of thermal cycling and also tapping and charging operations may

promote refractory erosion due to the collision of the charging materials with the lining.

Another problem related to the lining wear is the penetration of molten material into cracks

or joints. Thermal cycling not only induces stresses into the lining they also promote the

freezing and re-melting of the material deposited on the cracks, enlarging them to a point

where leaking of the molten material may produce run outs.

The major operational problems associated with embedded cooling systems are:

• Water leaking through the refractory lining, which in the worst case scenario may result

in catastrophic explosions due to the contact of cooling water with the molten metal. It

also may happen that the leaked water reacts with the process gas (especially SO

resulting in corrosion of the cooling devices, reducing their ability to extract heat.

• Uneven control of the wall heat transfer resulting in either increased refractory wear or

heat losses

• Air gaps formed as a result of the thermal cycles experienced by the furnace or due to

manufacturing problems of the cooling devices, causing loss of the cooling efficiency.

(a)

(b)

Fig. 1. Hot end of water cooled copper finger after being removed from a flash furnace. (a)

Front view, (b) lateral view. The dotted lines represent the original dimensions of the cooler.

Merry et al (Merry et al., 2000) offer similar data on the amount of heat that can be removed

with different cooling systems. Notice that in this compilation Merry et al, include finger

coolers. These cooling devices are in the mid range in terms of heat removal, they account